On the roadmap towards building a scalable, silicon-based quantum computer, several essential milestones have already been achieved. Most importantly: The development of a single-ion implantation technology that allows the precise placement of individual phosphorus atoms in silicon [1]; The application of advanced nanofabrication, microwave and low-temperature techniques to the production and characterization of Single Electron Transistors (rf-SETs), with a charge sensitivity close to the quantum limit [2]; The control and detection of single electron transfers between individual phosphorus donors [3], obtained by combining the single-ion implantation and SET techniques; and, The layout of quantum device structures for universal fault-tolerant quantum computation and the subsequent analysis of the error threshold [4,5].
In addition, the ability to locally apply strong microwave fields to the dopants in the channel of a small MOSFET, and detect the driven electron spin transitions by Electrically Detected Magnetic Resonance (EDMR) has been recently demonstrated [6].
The prior art will now be described in greater detail with reference to FIGS. 1, 2 and 3.
MOS-Based Silicon Quantum Dot and Rf-SET
Referring first to FIG. 1(a) and (c), the MOS-based silicon quantum dot structure 10 comprises a near intrinsic, high resistivity, silicon substrate 12. At either side of the device are regions 14 and 16 of phosphorus-diffused n+ areas, which provide ohmic contact to the device. A 5 nm thick layer of SiO218 is thermally grown on the surface. On top of this insulating oxide layer 18 two barrier gates 20 and 22 are fabricated using electron beam lithography (EBL), thermal evaporation of metal and liftoff. Each of the barrier gates 20 and 22 is ˜30 nm wide, and the separation between them is less than 40 nm. The barrier gates are partially oxidized using an oxygen plasma to create insulating layers 24 and 26 over their surfaces that are a few nanometers thick.
A top gate 28 is aligned to the barrier gates 20 and 22 during a second EBL stage, and again thermally evaporated and lifted off. The top gate 28 has a narrow neck region where it crosses over the top of the two lower gates 20 and 22; seen only in FIG. 1(a).
The top gate 28 is positively biased to create a gate-induced charge layer (GICL) 29, underneath the SiO2 layer 18; the n+-doped regions provide the charge for the accumulation layer. By further lowering the potential of the barrier gates, we isolate the small portion of GICL between the gates and obtain a quantum dot 30, whose coupling to the leads can be easily tuned by barrier gates 20 and 22 [7]. An example of bias spectroscopy of a single quantum dot is shown in FIG. 1(b).
Such a dot has a large charging energy and can be used as an rf-SET when connected to a resonant LC tank circuit. In this mode, a not yet fully optimized SET achieved a charge sensitivity of order 10 μe/(Hz)1/2 [8], which equals or surpasses that of typical aluminium SETs [2]. This exceptional charge sensitivity enables measurement of a charge transfer equivalent to 1% of an electron, with a measurement time of 10 μs.
When the device is inserted in a tank circuit, Coulomb blockade peaks FIG. 1(d) are obtained from the modulation of the reflected microwave power, see FIG. 1(e), when changing the potential of the top gate. The charge sensitivity achieved by biasing the device on the steepest slope of the Coulomb peaks is better than 10 μe/(Hz)1/2 [7,8].
The Si-SET has several important advantages, as compared to the more common Al-SETs. First, its fabrication is entirely MOS-compatible, since it does not require double-angle evaporation. Second, the thin (and nontunable) Al2O3 tunnel junctions—are replaced by tuneable barriers controlled by the gate potentials; this also reduces the vulnerability of the device due to uncontrolled or random electrostatic charges. Third, the Si-SET does not suffer from the difficulty of operating in magnetic fields of order 1 T, where Al-SETs undergo a transition from superconducting to normal state. Fourth, Si-SETs are immune to most of the charge offset noise that afflicts Al-SET devices [9].
Transport by Resonant Tunneling Through Single Dopants
The simplest structure we can devise to study individual dopants with the MOS-based structures described above, is a single tunnel barrier 20/22 interrupting a GICL 29, with a single dopant 44 implanted underneath the barrier gate, as sketched in FIG. 2. This device can be thought of as “half” of the Si quantum dot of FIG. 1, with the addition of a dopant under the barrier gate.
While varying the height of the tunnelling barrier for the charges, the barrier gate also has the function of bringing the dopant level in resonance with the Fermi level EF of the leads, see FIG. 2(c). In the presence of a magnetic field, the Zeeman-split dopant states can also be resolved. By applying a small source-drain bias and tuning the dopant level at resonance with the Fermi energies of the GICL, we expect to observe a very sharp conductivity peak, as recently demonstrated in similar experiments on finFETs [10] and Schottky devices [11]. A first observation of such conductivity peaks in this type of devices is shown in FIG. 2(d).
By inducing a Zeeman splitting of the electron or hole spin states (“spin down” 64, |↓>), and “spin up” 66, |↑>) with an external magnetic field, we can also demonstrate spin-dependent tunnelling, see FIG. 2(c), which is an essential ingredient for the single-shot measurement of spin qubit states. We note that, because of charging effects, the resonant charge tunnelling is sequential, that is, only one charge at a time can traverse the barrier by passing through the dopant level. Therefore, care must be taken to ensure that the transparency of the tunnel barrier is sufficient to yield a measurable current. We aim at tunnelling times ˜100 ns corresponding to currents of ˜1 pA. The drawing in FIG. 2(c) refers to the case where the dopant atom is a donor, and the charge carriers are electrons: the energy landscape should be mirrored in the case of acceptor atoms and holes.
Demonstration of Local Electron Spin Resonance (EDR) on Dopants
The coherent manipulation of the quantum state of a spin qubit requires the application of microwave fields, with a frequency matching the Zeeman splitting of the spin states. The ability to perform local ESR on a small number of dopants [6] has recently been demonstrated, by fabricating a MOS structure 50 where the top gate 52 has the double function of: (i) inducing a GICL in the MOSFET channel; and (ii) supplying the microwave field, see FIG. 3(a). For the latter purpose, the gate 52 is shaped as a coplanar transmission line, terminated by a short circuit. A microwave capacitor allows application of a microwave excitation to the line, in addition to the DC bias needed to induce the GICL. This arrangement yields maximum magnetic field in the channel of the MOSFET, and zero (microwave) electric field.
The absence of microwave electric field in the sensitive region is crucial to guarantee the proper operation of charge-sensing devices. Because there is no resonant structure, this ESR line can be used over an extremely wide frequency range (˜10 MHz to ˜50 GHz).
To verify the effectiveness of the local ESR line we have performed an EDMR experiment, where a weak but measurable spin-dependent scattering [12] of the conduction electrons with the P donors in the channel allows continuous monitoring of the electron spin polarization by measuring the conductance of the MOSFET. As shown in FIG. 3(b), we were able to observe all the expected features of the ESR of P donors, and (for the first time) to extend this type of investigation to the millikelvin temperature regime [6]. Notice the ability to resolve the hyperfine-split resonance peaks due to the interaction between the electron spin and the 31P nucleus. This demonstrates the excellent sensitivity of the design.
The next milestone is the coherent control and readout of the electron or hole spin of a single dopant in silicon. Two methods have been successfully demonstrated in GaAs quantum dots: the spin-to-charge conversion for single-shot readout of the electron spin state [13], and local Electron Spin Resonance (ESR) [14] for the coherent manipulation of the spin state. Apart from demonstrating these in silicon devices, another ingredient that has not yet been finalized is an optimal charge reservoir for spin-dependent tunnelling to- and from- a single dopant. Up until this time, the focus for this ingredient has been directed to nanometer-sized Schottky contacts of platinum silicide.